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• W2538110817 abstract "We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general case with noisy observations, we show that our algorithm is guaranteed to linearly converge to the unknown low-rank matrix up to minimax optimal statistical error, provided an appropriate initial estimator. While in the generic noiseless setting, our algorithm converges to the unknown low-rank matrix at a linear rate and enables exact recovery with optimal sample complexity. In addition, we develop a new initialization algorithm to provide a desired initial estimator, which outperforms existing initialization algorithms for nonconvex low-rank matrix estimation. We illustrate the superiority of our framework through three examples: matrix regression, matrix completion, and one-bit matrix completion. We also corroborate our theory through extensive experiments on synthetic data." @default.
• W2538110817 created "2016-10-28" @default.
• W2538110817 creator A5002318539 @default.
• W2538110817 creator A5051448391 @default.
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• W2538110817 date "2016-10-17" @default.
• W2538110817 modified "2023-09-22" @default.
• W2538110817 title "A Unified Computational and Statistical Framework for Nonconvex Low-Rank Matrix Estimation" @default.
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• W2538110817 hasPublicationYear "2016" @default.
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